Echoes of past encounters with leukemia flow through the veins of people who have never suffered from the disease, a study suggests. The immune systems of cancer-free people may have gathered antileukemia forces by mounting preemptive strikes against cells that were on their way to becoming cancerous. Leukemia patients, on the other hand, carry meager signs of resistance.

“Perhaps we’ve all had a bit of precancerous disease,” says immunologist Mark Cobbold of the University of Birmingham in En...